ID: 2111.05751

On a girth-free variant of the Bourgain-Gamburd machine

November 10, 2021

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Ilya D. Shkredov
Mathematics
Number Theory
Combinatorics

A variant of the Bourgain-Gamburd machine without using any girth bounds is obtained. Also, we find series of applications of %our result the Bourgain-Gamburd machine to problems of Additive Combinatorics, Number Theory and Probability.

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